An inequality between class numbers and Ono's numbers associated to imaginary quadratic fields
Sairaiji, Fumio ; Shimizu, Kenichi
Proc. Japan Acad. Ser. A Math. Sci., Tome 78 (2002) no. 10, p. 105-108 / Harvested from Project Euclid
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Ono's number $p_D$ and the class number $h_D$, associated to an imaginary quadratic field with discriminant $-D$, are closely connected. For example, Frobenius-Rabinowitsch Theorem asserts that $p_D = 1$ if and only if $h_D = 1$. In 1986, T. Ono raised a problem whether the inequality $h_D \leq 2^{p_D}$ holds. However, in our previous paper [8], we saw that there are infinitely many $D$ such that the inequality does not hold. In this paper we give a modification to the inequality $h_D \leq 2^{p_D}$. We also discuss lower and upper bounds for Ono's number $p_D$.
Publié le : 2002-09-14
Classification:  Ono's number,  class number,  11R11,  11R29 
@article{1148392629,
     author = {Sairaiji, Fumio and Shimizu, Kenichi},
     title = {An inequality between class numbers and Ono's numbers associated to imaginary quadratic fields},
     journal = {Proc. Japan Acad. Ser. A Math. Sci.},
     volume = {78},
     number = {10},
     year = {2002},
     pages = { 105-108},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1148392629}
}

Sairaiji, Fumio; Shimizu, Kenichi. An inequality between class numbers and Ono's numbers associated to imaginary quadratic fields. Proc. Japan Acad. Ser. A Math. Sci., Tome 78 (2002) no. 10, pp.  105-108. http://gdmltest.u-ga.fr/item/1148392629/